Probabilistic Aspects of Error Growth In Atmospheric Dynamics

A probabilistic approach accounting for the variability of error growth in the atmosphere is developed and applied to an idealized low‐order atmospheric circulation model. Error growth in a single‐realization, ensemble‐averaged error versus time and the time‐dependent as well as the asymptotic probability distribution of errors are determined. A wide dispersion around the mean is found, showing clearly the inadequacy of a description that is limited to averaged properties only. A self‐consistent one‐variable, two‐parameter model of error dynamics is constructed in the form of a stochastically driven logistic equation, and the results are shown to be in good quantitative agreement with the simulation of the full equations. A generalization to more realistic atmospheric models is also outlined.